A consistent finite element formulation for non‐linear dynamic analysis of planar beam

Kuo Mo Hsiao*, Rong Tser Yang, An-Chen Lee

*Corresponding author for this work

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

A co‐rotational finite element formulation for the dynamic analysis of planar Euler beam is presented. Both the internal nodal forces due to deformation and the inertia nodal forces are systematically derived by consistent linearization of the fully geometrically non‐linear beam theory using the d'Alembert principle and the virtual work principle. Due to the consideration of the exact kinematics of Euler beam, some velocity coupling terms are obtained in the inertia nodal forces. An incremental‐iterative method based on the Newmark direct integration method and the Newton–Raphson method is employed here for the solution of the non‐linear dynamic equilibrium equations. Numerical examples are presented to investigate the effect of the velocity coupling terms on the dynamic response of the beam structures.

Original languageEnglish
Pages (from-to)75-89
Number of pages15
JournalInternational Journal for Numerical Methods in Engineering
Volume37
Issue number1
DOIs
StatePublished - 1 Jan 1994

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